Use render layers in sequence editor
Load the EXR as an image sequence into the compositor of another scene. Route the layers that you want to the Compositor Output Node. Then load that scene as a strip into the VSE scene timeline. Do this for each layer of the EXR that you want to combine. Remember that in the VSE you will need to enable Linear to mix the EXR as they probably are not scene referred.

Make an EXR with multiple outputs:



Then import them into a compositor and route each layer to comp output using 1 scene per layer.



Then mix them as required in the VSE. The VSE isn't really ideal for this to be honest.